Entries by stevendaryl

In introductory physics, the optics unit often teaches about virtual and real images, focal lengths, indexes of refraction, etc. Some questions that are sometimes glossed over in the rush to present the mathematical formulas and definitions is: What does it mean for an image to form at a particular location? What does it mean for […]

This little trick is used for some integration problems involving trigonometric functions is probably well-known, but I only learned it yesterday. So under the assumption that others don’t know it, I will share my insight. When you take calculus, one of the most mysterious integrals is this one involving the secant: ∫ sec(θ) dθ = log(sec(θ) […]

This is a little note about quantum amplitudes. Even though quantum probabilities seem very mysterious, with weird interference effects and seemingly nonlocal effects, the mathematics of quantum amplitudes are completely straight-forward. (The amplitude squared gives the probability.) As a matter of fact, the rules for computing amplitudes are almost exactly the same as the classical […]

Everybody learns the “quadratic formula” for solving equations of the form [itex]A x^2 + B x + C = 0[/itex], even though you don’t really need such a formula, because you can solve for [itex]x[/itex] through the technique of “completing the square”. What you need a formula for is the solution to the cubic equation: […]